The Internet retailing giant declines to reveal actual sales figures for the Kindle Fire, which it released last year in the run up to the holiday sales season. That leaves its market share open to speculation, CNN Money notes.

Most industry tracking firms say the Kindle Fire started off strong last year, but faded after the Christmas shopping season, and has lagged since. IHS Suppli, for instance, reports that the Kindle Fire never accounted for more than 14% of overall tablet sales.

IHS says that Apple‘s (NASDAQ:AAPL) iPad currently comprises more than 66% of the tablet market, followed by Samsung tablets at 9%, and, in third place, Amazon with just 4% of tablet sales.

Amazon, however, says the Kindle Fire made up 22% of tablet sales in the U.S. since its release. If accurate, that would make it the strongest competitor to Apple’s market-dominating iPad, whose 9.7-inch basic model, priced at $499, is more than twice as expensive as the 7-inch $199 Kindle Fire.

But Apple may be planning to give Amazon a run for is smaller-screen money. In October, the iPad maker will reportedly debut is own 7.85-inch tablet — the iPad Mini — priced well below its standard-sized iPad kin.

An iPad Mini is clearly meant to take on the Kindle Fire and a number of other small-screen tablets running Google‘s (NASDAQ:GOOG) Android operating system. It also suggests that Apple has changed its mind about whether a significant market exists for smaller tablets.

Amazon may not take that lying down, though. Having trod on iPad territory with the Kindle Fire, rumors are circulating that the company may also introduce a 10-inch Kindle Fire to go along with the 7-inch version.